Statistics And Probability Question 545

Question: The two events A and B have probabilities 0.25 and 0.50 respectively. The probability that both A and B occur simultaneously is 0.14. Then the probability that neither A nor B occurs is

[IIT 1980; MP PET 1994]

Options:

A) 0.39

B) 0.25

C) 0.904

D) None of these

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Answer:

Correct Answer: A

Solution:

  •                  $ P(A^{c}\cap B^{c})=1-P(A\cup B) $                                                   $ =1-[0.25+0.5-0.14]=0.39. $